Author: Chris Webster

In meteorology, the quantity pressure is an important driver of physical processes in the atmosphere. Pressure is the force applied over a unit of area, so it can be increased by having more force acting over a smaller area. Pressure is measured in Pascals, named after the French mathematician and physicist Blaise Pascal (who also devised the famous “Pascal’s triangle”). The abbreviation for Pascal is Pa.

An example of where air has high pressure is the inside of an inflated tyre. For typical values of air pressure in a tyre, it’s best to measure pressure in units of kilopascals (kPa, thousands of Pascals). But for the range of air pressures that occur naturally in the atmosphere we normally use hectoPascals (hPa, hundreds of Pascals) rather than kPa. At the Earth’s surface the air pressure of the atmosphere is usually within the range 980 to 1030 hPa.

The hectoPascal is the modern replacement unit for the millibar:

one hPa = one millibar = one thousandth of a “bar”.

The millibar was introduced by the British meteorologist Sir Napier Shaw in the early 1900s. Shaw also created an important thermodynamic diagram that is still used extensively today in modern meteorological services worldwide.

In 1930 Shaw sent his Christmas greetings to the then director of the NZ Meteorological Service, Dr Edward Kidson. A copy of the card is reproduced below.

This is in illustration of a new view (so far as I am concerned) of the relation between velocity and pressure gradient namely that it is the velocity that controls the gradient. If it increases, the gradient will increase so motion round an area means the creation of high pressure over the area. The picture is for the northern hemisphere.

What is fine weather for you? Anticyclonic as here, or cyclonic? I have just sent off the last of M.S. for Vol iv : shall have time to write soon.

Sir Napier Shaw

(The reference to “Vol iv” relates to a manual of meteorology that Shaw had been working on for some time. “Aeolian” relates to Aeolus, the Greek god of wind)

I can most readily illustrate the importance of air pressure to weather by referring to today’s weather map:

Mean Sea Level analysis, 6am 3 July (18UTC 2 July) 2014

The thin solid lines are isobars, which means lines connecting places with equal air pressure (note the “bar” in “isobar”). These lines give a good idea of what the broad-scale winds are.

Let me explain by describing what happens when you release the valve on a tyre. The air ejects from the region of much higher pressure within the tyre to the region of lower air pressure outside the tyre. In the Earth’s atmosphere, when the air accelerates from high to low pressure, the rotation of the Earth deflects the out-flowing air towards the left in our southern hemisphere (the opposite deflection occurs in the northern hemisphere). This is why the air around an anticyclone (High pressure area) rotates anticlockwise in our hemisphere. A previous blog-post describes the anticyclonic outflow of anticyclones, together with the descent that is characteristic of Highs.

At the time of the chart above, NZ was mostly affected by a southwesterly air-stream (i.e. coming from the southwest, and therefore cold). In this chart the spacing between the isobars is 4 hPa.

If we remove the fronts from the chart and increase the number of isobars by drawing them at 1 hPa spacing, we get an increased level of detail about the pressure field, as below:

Chart at same time as previous, but fronts removed and intermediate isobars added (in grey)

Note, for example, the extra detail about the structure of the High over New South Wales and Victoria.

Thinking about the tyre again, when you initially release the valve the difference in air pressure between each side of the valve is large – the air rushes out with a hiss. If you were to continue deflating the tyre, the difference in air pressure would reduce and the air-flow would become much gentler. Similarly, in the atmosphere, when the isobars are close together the air rushes out faster and gets deflected more – thus the winds are stronger when the isobars are close together.

Less obvious is how air pressure changes as you go up in the atmosphere. For example, if you were flying to Australia the ambient air pressure as you cruised across the Tasman Sea would be about a quarter of what you’d experience at the sea surface. You can read more about these vertical variations at this blog post: http://blog.metservice.com/2011/11/up-and-away/.

When recruiting and training people to become meteorologists, MetService requires that trainees hold a university science degree in maths and physics. Why maths and physics?

First and foremost, meteorology is a science, and we need people in our National Forecast Centre who are capable of applying the scientific thinking that they’ve developed at university to understand the state of the atmosphere.

Let’s look at specific examples of why maths and physics are important to meteorology.

The physics of fog

Forecasting for aviation generally has a low profile as far as the general public is concerned, but it is critical for airlines and pilots for safe and efficient air travel. There are many meteorological phenomena that impact flying, e.g. thunderstorms, turbulence, air frame icing and cross winds on landing. One of the most critical is fog because of the severe reduction in visibility it can cause.

It is a fundamental property of moist air that (invisible) water vapour changes into (visible) water when the vapour content reaches a threshold value that depends critically on temperature.

The existence of this threshold makes fog forecasting one of the hardest of all weather phenomena to predict. Fog formation can sit on a knife edge. For example, under suitable conditions fog can form when the air temperature cools to, say, 7 deg C, but if it were to cool to only 8 deg C there’d be no fog. Almost a binary situation, and the difference in how far you can see could drop from 50 km to 500 metres with the extra degree of cooling.

When our aeronautical meteorologists forecast fog at New Zealand airports they apply maths and physics, including the principles of thermodynamics, radiative processes, graphs (of cooling rates), and statistics (of airport climates). A basic example of a cooling rate graph is below.

Actual (red) and predicted (orange) temperature, Christchurch International Airport, for overnight hours of 20 and 21 March 2013 (blue line is dew point temperature). The horizontal lines indicate fog formation thresholds. UTC time is 13 hours earlier than NZ Daylight Time, so 20 05 is 6pm local time, 20 15 is 4am and so forth.

Here, the forecaster needs to assess what the overnight temperature will in fact cool to, to form this type of fog (there are other types) based on the available guidance, and decide if there will be enough water vapour present to form the fog.

Probability and Statistics

The basic concepts of probability and statistics are introduced in maths at school. Meteorology is an inexact science and, every day in the National Forecast Centre, scientists are forming hypotheses about future weather outcomes around NZ. The concept of hypothesis testing is usually introduced in Year 13 mathematics with statistics, and further developed at university.

Currently most public weather forecasts in New Zealand state a single expected outcome rather than the range of viable outcomes. This is great in terms of delivering a short forecast but, unfortunately, misses out valuable information about the other viable outcomes that depend on the state of the atmosphere at the time. Some of our forecast users address this by obtaining information expressed as statistical probabilities, for example, as a probability distribution. In the future, I think it’s likely that public weather forecasts will adapt to an increasing need for probabilistic information.

The meteorologist assesses cloud-top temperatures in segments of the spiral, providing an objective gauge about the cyclone’s intensity.

Remember trigonometry from school? This branch of maths is important in many sciences. An example related to meteorology is spherical trigonometry, in which any location on Earth can be specified in terms of latitude, longitude and height above the Earth’s surface. Our weather radars make extensive use of the principles of trigonometry to determine the location and movement of precipitation targets.

Rates of change (differentiation)

The concept of rate of change occurs all the time in meteorology. It occurs on many scales, e.g. in less than an hour with the fall of temperature during the passage of a cold front, or over a few days with the decrease of air pressure in an intensifying depression.

In an earlier blog post (Year 12 maths) I gave an example of the importance of maths to meteorology. In mathematics, a rate of change is called a differential or derivative (ask someone doing Year 12 maths!). To describe the motion of air using the techniques of fluid mechanics (a branch of physics and applied maths), many equations containing differentials crop up. It turns out that, because of chaos theory, there are no easy ways to solve these equations. But all is not lost…

Numerical analysis

A hundred years ago, a brilliant Englishman called Lewis Richardson found a way to approximate solutions to the equations of air motion. Nowadays, with the benefit of a new branch of mathematics called numerical analysis and increasingly powerful computers, we can solve the equations accurately up to several days ahead. Just how accurately depends on the state of the atmosphere at the time, but sometimes it’s possible to predict the development and path of a depression before it has formed.

The computers that are required are extremely powerful. The best ones, called super-computers, are found in overseas meteorological centres. Data transfer between continents isn’t a big issue these days, so data from these centres is routinely sent to us so that NZ forecasts benefit from the fruits of Richardson’s pioneering work.

Sir Isaac Newton’s laws of physics

I referred to fluid mechanics earlier. Some of the most important equations in fluid mechanics are tailored versions of Newton’s second law of motion (Force = mass x acceleration). Physics again!

Here’s one of the equations of motion based on Newton’s work:

The symbols are:

The rate of change of the eastward wind is the acceleration, and the terms on the right-hand side of the equation are the forces acting on the air mass.

International standards of training

The World Meteorological Organisation (WMO) prescribes the educational standards for meteorologists (WMO 1083). A good grounding in both mathematics and physics is essential to achieve this internationally recognised standard.

If you or someone you know of is thinking of becoming a meteorologist, and wondering what they need to study, tell them to keep up their maths and physics at school, and continue with them through to university.

In the English language we have many words in common usage that have related but more specific meanings in a scientific and mathematical context. The key word of this blog post, “convergence”, is a good example of this.

We sometimes hear of people’s views on some matter initially disagreeing and then, at a later time, coming together or “converging”. In fluid dynamics we’re often interested in regions where different air flows come together. We call this type of flow convergence, and say that the air is converging. It’s an important concept in meteorology because convergence often has a big effect on weather conditions, driving where the cloud is (or isn’t). Sometimes, in suitable conditions, it leads to heavy showers and thunderstorms. Let’s take a closer look at convergence.

In its purest form, air that’s coming together would look like the graphic below, where the arrows show how the air is moving. Everywhere in this graphic the air flow is converging.

A field of pure convergence.

For example, in the centre where the arrows are all pointing inwards, the air flow is clearly coming together. More subtly, if you’ve got a good spatial imagination you might be able to spot another kind of convergence … run your eyes along one of the radial lines coming in towards the centre. A longer arrow indicates stronger wind and, even when there’s no change in direction, at each point along the radial the flow is convergent because there’s more air flowing in than flowing out. That is, convergence can be caused by speed effects as well as directional effects. Send me a comment if you’d like me to explain this further

The opposite of convergence is divergence. In air flows aloft (in the upper atmosphere), meteorologists are often interested in upper divergence because it draws air upwards from underneath. Such regions usually have a big influence on the kinds of weather systems that bring stormy weather to NZ. But that’s another story; let’s get back to convergence.

Sea-breezes form on clear summer days when the land heats up more than the adjacent sea. The result is a cooling wind that flows at low-levels from the sea onto the land.

Around Northland and Auckland, we can have these sea-breezes occurring along the entire coastline, both west and east coasts. Because the land mass separating these coastal regions is quite narrow, convergence occurs when sea-breezes coming from opposite directions meet, as in the picture below.

Converging see-breezes on a clear summer day over Northland and Auckland.

Where the air comes together, it has to go somewhere. In the atmosphere, when air converges at low-levels, it gets pushed upwards. Provided that there’s enough moisture in the air, the uplift will generate cloud and potentially precipitation too. If the air is unstable (see Predictability & popcorn) the convergence can generate convection in the form of cumuliform cloud and showers.

As for previous figure, with the effect of rising air included.

Here’s a good example from 31 January 2012. The animation of satellite imagery below shows the distribution of cloud from mid-morning till early evening that day. As the sea-breezes developed and came together, a very prominent line of cloud formed along the middle of Northland and the Auckland isthmus.

There are other ways that air can come together in the atmosphere. The earlier post on Cloud Structures over NZ on 26 July showed the effect of air that was channeled by the topography. Air was flowing westwards through Cook Strait and the Manawatu Gorge area. As the low-level flow spread out downstream, a line of convergence was created where the air came together over the sea west of Manawatu. A similar effect generated a line of convergence over Bay of Plenty.

Convergence also occurs on bigger scales. The chart below shows typical low-level wind flows over the southwest Pacific during summer. Where the Trade winds come together there’s a zone of convergence called the Inter Tropical Convergence Zone (ITCZ). A secondary zone of convergence runs from near Vanuatu east-southeastwards through the Cook Islands, and is called the South Pacific Convergence Zone (SPCZ).

Typical low-level flows over the southwest Pacific during summer.

Both of these zones are associated with increased cloudiness and showers of varying intensity, depending on the state of activity of the zone at any time. The positions of the zones shift around too in response to various influences. As we approach the summer months its pertinent to point out that Tropical Cyclones form over the southwest Pacific Ocean from disturbances associated with tropical convergence zones.

The inward flow in depressions causes convergence and lifting of air over a wide area above depressions. As stated above, rising air favours cloud and precipitation. This is why depressions (Lows) are generally associated with cloudy and often rainy or showery weather.

At the beginning of this post I referred to how convergence drives where cloud is and isn’t. A nice example of the latter comes with the sea-breeze. Over the sea where the air starts flowing towards land, the low-level air is divergent. This drives the air aloft downwards towards the water, and creates generally cloud free conditions. A useful tip if you’re an aircraft pilot wanting to avoid cloud on a cross-country flight in the vicinity of a coastline.

I hope you can see why meteorologists are interested in where and when convergence occurs!

On Thursday 26 July 2012 a cold southeasterly airstream flowed onto the North Island, around an anticyclone centred just east of the South Island. In this blog post we’ll look at some interesting small-scale cloud structures around the country on this day.

Below is the weather map at midday on Thursday 26 July. The red arrows show the sense of the broad-scale rotation around the anticyclone.

While the North Island was experiencing a southeasterly flow, the isobars were widely spaced over the South Island, indicating little wind there. Take a look at the animation below, based on visible light as received by the MtSat-2 geostationary satellite.

As explained in the post on the effect of resolution, the visible satellite image shows all cloud as white or light grey, regardless of how high or low the cloud is. Most of the cloud over New Zealand is on the east coast of the North Island. Just off the Manawatu coast there is a plume-shaped area of cloud that extends northwestwards parallel to the flow. This is low-level cloud in a region where the air flow near the Earth’s surface is coming together, or converging. As the air convergences it is forced to rise and, with enough moisture, cloud forms.

There is a similar process occurring off eastern Bay of Plenty. In this case there is a zone of more concentrated convergence that shapes the clouds into a rope-like appearance, but the orientation of it is still towards the northwest and parallel to the flow.

Most of the South Island is cloud-free, but there is a patch of grey-looking cloud around Lakes Tekapo and Pukaki. This is also low cloud, but it has formed during the night in the valleys and basins. In the afternoon there’s been just enough heat from the weak winter sun to break up and disperse the cloud. The cloud base at Pukaki during the morning was reported as being about 600 metres above the ground – the air temperature had risen from minus 4 overnight to plus 3 by lunchtime.

The Terra polar-orbiting satellite has a very high resolution sensor. Terra passed over New Zealand within the period of the previous images, and I’ve reproduced the image below, split into two colour images.

Very high resolution satellite image within the period of the previous images. Image courtesy of MODIS Rapid Response Project, NASA/GSFC.

The features discussed above are very apparent. The area of convergence off Manawatu evidently has a double structure, and it is striking how this high resolution image shows individual cumulus clouds as white dots (as discussed in the previous post). There are cloud streets over the central North Island from the Kaweka to the Raukumara ranges.

Over the Pacific ocean there is a lot of cloud having a cellular structure. This is typical of a cold body of air that moves onto relatively warmer water. The air bubbles up into cumulus clouds that tend to clump together into ring-shaped clusters.

The low cloud over Lakes Tekapo and Pukaki (below) has a flat appearance typical of layered stratus cloud. It extends its fingers into the valleys between the peaks of the surrounding ranges.

As previous image, but for South Island.

The cloud over the ocean east of Canterbury is stratocumulus, a combination of the lumpy texture of cumulus cloud and the layering of stratus cloud. In many respects there was nothing particularly unusual about our weather on 26 July, but the satellite images were still able to reveal some fascinating and beautiful cloud structures.

New Zealand’s weather is currently dominated by a large anticyclone that’s bringing fine sunny weather and light winds to many areas.

The chart below shows the position of the centre of the anticyclone at midday Tuesday 10 July 2012. The red arrows show the sense of the broad-scale rotation around the system (anticlockwise in the Southern Hemisphere). It also shows the smaller-scale flow around the top of the South Island, and how this is directed onto Manawatu and Wellington. There are some subtle aspects to this flow that I’d like to investigate in this blog post, using satellite imagery.

Weather map at midday 10 July 2012.

The term resolution is used to describe the capability to distinguish between objects sitting next to each other. High resolution means that objects that are close together can be separately identified, whereas lower resolution means you can’t tell that there’s more than one object. The term resolution can refer to the number of pixels in a computer monitor or dots-per-inch of a printer. It also refers to the amount of detail that can be discerned in an image from a weather satellite.

Take a look at the image below, based on visible light as received by the MtSat-2 geostationary meteorological satellite.

The image covers a large area, and it shows patchy cloud over and around New Zealand. Because the image uses visible wavelengths of light, it shows all cloud as white or light grey, regardless of how high or low the cloud is. This differs from infrared images, the ones usually displayed on TV and on websites, which show high cold clouds more prominently than the lower (and warmer) clouds.

Central Australia is largely cloud-free, and there are variations in the shades of grey caused by the varying texture of the land surface there. Over Queensland there is cloud with a wispy, fibrous texture. This is cirrus, composed of ice crystals which give it this appearance. It’s not possible to see much detail in the cloud over New Zealand. Note that the southeast corner of this image is darkened, due to the setting sun there.

The same satellite can provide us with higher resolution visible imagery over New Zealand as below, valid for the same time as the previous image.

We can now see that there’s quite a bit of cloud over Fiordland and Southland, and a few patches around north Westland, Manawatu and Wellington. Most of this cloud is at low-levels, typically stratocumulus and low-topped cumulus. Notice how the cloud seems to swirl around Farewell Spit and then towards the lower North Island. You might just be able to pick up a little of the structure of the few clouds that there are over Wairarapa.

The Aqua polar-orbiting satellite has a very high resolution sensor, capable of providing visible imagery to a resolution of 250 metres. Because this satellite orbits the Earth from Pole to Pole, the images are only available for places that the satellite passes over. Fortunately, Aqua passed over New Zealand at about the same time as the previous images, and I’ve reproduced the image below (converted to black and white to aid comparison). The richness of detail is striking.

Very high resolution satellite image for approximately same time as previous images. Image courtesy of MODIS Rapid Response Project, NASA/GSFC.

Stratocumulus covers Manawatu, and transitions into a lumpier looking cumulus structure to the north near Wanganui. There is banding in the cumulus as it approaches the gap between the Ruahine and Tararua ranges, the area surrounding the Manawatu Gorge. The stratocumulus and cumulus cloud has been enhanced by the air having been forced to rise on the western (windward) side of the Tararua ranges (see post on Foehn wind). On the eastern (leeward) side the skies are mostly cloud free, indicating a sunny winter’s day.

The smaller Puketoi range east of the Gorge provides another smaller-scale environment for enhancing the cloud on the windward (western) side. The image also shows snow lying on the tops of the Ruahine and Tararua ranges.

The banding I talked about earlier is called “cloud streets”: the cumulus clouds are organised into longitudinal rolls by the low-level wind-flow. There’s further evidence of banding east and northeast of the Puketoi range, with curvature indicating the shape of the wind-flow as it exits the Gorge bottle-neck and spreads out. The resolution of this image is so high that you can see (or resolve) individual cumulus clouds as small white dots.

On Thursday 19 April, New Zealand was completely surrounded by a very large High (or anticyclone).

The air pressure at sea level was above 1030 hPa everywhere over New Zealand at midday on Thursday. Highest pressures were over inland Otago and Canterbury, peaking at 1039 hPa. Christchurch Airport was reporting 1038.2 hPa … that’s very high indeed.

Here is a sequence of weather maps showing how the anticyclone developed over preceding days (click on the image to view animation). The first map is from midday on Thursday 12 April, and the time steps are six hours until the final map at midday on Thursday 19 April. It’s interesting how the initial anticyclone moved onto the Tasman Sea with a central pressure around 1029 to 1030 hPa, then another system came up from the Tasmania region and joined the initial system, reinforcing it.

Sequence of weather maps, 12 to 19 April 2012.

This anticyclone was bringing clear, sunny weather to many places, just as typical barometers indicate on their dials when the air pressure is high. However, there were many places, particularly along eastern coasts, where the weather was not sunny at all. In fact there was even some light rain about.

Take a look at the satellite image below for details of where cloud was on the late morning of Thursday 19 April.

Image courtesy of MODIS Rapid Response Project, NASA/GSFC.

There was a lot of cloud over eastern regions, especially the east of North Island. The satellite picture showed some beautiful cloud forms over eastern Bay of Plenty… these are low clouds shaped by a combination of waves in the lee of the ranges and orientated perpendicular to the flow, and streets of cloud that are parallel to the flow.

Having looked at the clouds from above, let’s also look at them from below. I took this photo of the clouds over the eastern hills of Wellington in the late afternoon of Thursday 19 April, after a rather grey cloudy day in the capital. The barometer was indicating around 1036 hPa.

Why is it that not all Highs bring sunny weather? It’s all to do with the upward and downward motions associated with them. Anticyclones generate sinking motion of air, as described in an earlier blog post . As the air sinks it becomes drier, and any cloud in it will generally evaporate. But this sinking air doesn’t make it all the way to the ground and, in the case of the current anticylone over New Zealand, there was a lot of moist air and cloud trapped just above the Earth’s surface.

Most of us live within a few hundred metres of sea level. If we are beneath this anticyclonic cloud, all we see is a cloudy day, even though the skies are blue above. If there’s enough low-level moisture the clouds can generate light rain or drizzle too, though it doesn’t come to much.

Wherever the wind at low levels is blowing from the sea onto the coast, it’s more likely that the air will be moist enough to bring cloud. That was the case for most eastern parts of New Zealand on Thursday 19 April. And there were some patches of drizzle and light rain about too.

Most places in the west were sheltered from the low level flow, and were indeed getting clear sunny weather.

So, with some interpretation, it’s possible to deduce quite a bit from what the barometer is measuring!

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